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English version: Journal of Applied and Industrial Mathematics, 2016, 10:3, 380385 

Volume 23, No 3, 2016, P. 8192 UDC 519.716
Keywords: maximal subalgebra, unary recursive function. DOI: 10.17377/daio.2016.23.518 Sergei S. Marchenkov ^{1} Received 3 December 2015 References[1] S. A. Berezin, An algebra of unate primitive recursive functions with iteration operation of general form, Kibern., No. 3, 12–19, 1976. Translated in Cybern., 12, No. 3, 346–353, 1976.[2] S. A. Berezin, Maximal subalgebras of recursive function algebras, Kibern., No. 6, 123–125, 1978. Translated in Cybern., 14, No. 6, 935–938, 1978. [3] G. P. Gavrilov, On functional completeness in a countablevalued logic, in A. A. Lyapunov, ed., Problemy kibernetiki (Problems of Cybernetics), Vol. 15, pp. 5–64, Nauka, Moscow, 1965. [4] A. Grzegorczyk, Some classes of recursive functions, in Rozprawy Matematyczne (Mathematical Apparatus), Vol. 4, Pol. Tow. Mat., Warsaw, 1953. Translated in Problemy matematicheskoi logiki (Problems of Mathematical Logic), pp. 9–49, Mir, Moscow, 1970. [5] V. V. Koz’minykh, On primitive recursive functions of a single argument, Algebra Logika, 7, No. 1, 75–90, 1968. Translated in Algebra Logic, 7, No. 1, 44–53, 1968. [6] S. S. Marchenkov, A method for constructing maximal subalgebras of algebras of general recursive functions, Algebra Logika, 17, No. 5, 581–595, 1978. Translated in Algebra Logic, 17, No. 5, 383–392, 1978. [7] S. S. Marchenkov, On cardinality of the set of precomplete classes in some classes of a countablevalued logic, in S. V. Yablonskii, ed., Problemy kibernetiki (Problems of Cybernetics), Vol. 38, pp. 109–116, Nauka, Moscow, 1981. [8] S. S. Marchenkov, Elementarnye rekursivnye funktsii (Elementary Recursive Functions), MTsNMO, Moscow, 2003. [9] S. S. Marchenkov, Funktsional’nye sistemy s operatsiei superpozitsii (Functional Systems with Superposition Operation), FIZMATLIT, Moscow, 2004. [10] V. L. Mikheev, Class of algebras of primitive recursive functions, Mat. Zametki, 14, No. 1, 143–156, 1973. Translated in Math. Notes Acad. Sci. USSR, 14, No. 1, 638–645, 1981. [11] R. W. Ritchie, Classes of predictably computable functions, Trans. Amer. Math. Soc., 106, No. 1, 139–173, 1963. Translated in Problemy matematicheskoi logiki (Problems of Mathematical Logic), pp. 50–93, Mir, Moscow, 1970. [12] M. G. Rozinas, An algebra of manyplaced primitive recursive functions, in Uchenye zapiski Ivanovskogo gosudarstvennogo pedagogicheskogo instituta (Scientific Notes of Ivanovo State Pedagogical Institute), Vol. 117, pp. 95–111, ISPI, Ivanovo, 1972. [13] V. A. Sokolov, Maximal subalgebras of the algebra of all partially recursive functions, Kibern., No. 1, 70–73, 1972. Translated in Cybern., 8, No. 1, 76–79, 1972. 

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